# White noise DC component

I'm really new to DSP, I'm actually studying Computer Science and took an elective on DSP so my knowledge is pretty limited.

I've learned that pure white noise signal for example has all possible frequencies, that means that it also has zero frequency so it has a non zero DC component(does that mean it?) but pure white noise by definition has a zero mean and thus has a zero DC component..
What am I missing?

Thanks!

• The value of a signal's PSD at $f=0$ is not the same thing as the signal's DC value; see dsp.stackexchange.com/questions/21583/… – MBaz Feb 17 '17 at 22:24
• These are two separate questions. Therefore they should be asked separately. – Tendero Feb 17 '17 at 22:50
• @MBaz I see.. so does that mean that DC component is in time domain and the component at $f=0$ is in frequency domain and thus they have different values? Or is it something else? – Evgeny A. Feb 17 '17 at 22:51
• @Tendero Yeah I thought so.. should I split it now? – Evgeny A. Feb 17 '17 at 22:54
• @EvgenyA. I just edited your post to left only one of them. Please feel free to ask the other one in a different post. – Tendero Feb 17 '17 at 22:55

White noise has no component at any specific frequency since it is a noise density and therefore has energy across a range of frequencies. The range of any given specific frequency, including DC is zero, and therefore the energy at DC (and any specific frequency) is indeed zero.

In practice you cannot actually observe DC or any specific frequency as a single point as that would require an infinite observation time. However, the longer you observe, the narrower will be the effective range of frequencies you observe and for this reason the mean will be non-zero but approach zero as your observation time approaches infinity.